#2851 ⟨a, b, c | aaa=b, cbc=a⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Isomorphic instances

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. ca4 ⇒ a4c [3]
2. ca3c ⇒ a [2]
3. b ⇒ a3 [1]
# abc:aaa=b,cbc=a ac/b - -
caaaa=aaaac
caaac=a
b=aaa

Other submonoids of same group

10 unique, 114 total

Σ#PresentationPropertiesφ
7366⟨a, b, c | aba=b, cbc=1⟩Grp Inf93
7548⟨a, b, c | bb=aa, cc=a⟩Can Inf1
7938⟨a, b, c | aa=b, cbc=b⟩Can Inf5
82849⟨a, b, c | aaa=b, cac=b⟩Can Inf2
83041⟨a, b, c | aba=b, cac=b⟩Can Inf
83042⟨a, b, c | aba=b, cbc=a⟩Can Inf1
83472⟨a, b, c | ba=ac, cab=a⟩Can Inf
83501⟨a, b, c | bb=ac, aaa=c⟩Can Inf2
83594⟨a, b, c | ba=ac, cb=aa⟩Can Inf
86095⟨a, b, c | ab=c, bcc=ca⟩Can Inf

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

3 total

Σ#PresentationMapping
82980⟨a, b, c | aab=c, bac=a⟩φ(a) = a, φ(b) = c, φ(c) = aac
85259⟨a, b, c | aa=b, cabc=a⟩φ(a) = a, φ(b) = aa, φ(c) = c
85557⟨a, b, c | ab=c, baac=a⟩φ(a) = a, φ(b) = c, φ(c) = ac